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Approximate Distributions of Order Statistics

With Applications to Nonparametric Statistics

  • R.-D. Reiss

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. R.-D. Reiss
      Pages 1-8
  3. Exact Distributions and Basic Tools

    1. Front Matter
      Pages 9-9
    2. R.-D. Reiss
      Pages 64-82
  4. Asymptotic Theory

    1. Front Matter
      Pages 105-105
    2. R.-D. Reiss
      Pages 206-228
    3. R.-D. Reiss
      Pages 229-239
  5. Statistical Models and Procedures

    1. Front Matter
      Pages 241-241
    2. R.-D. Reiss
      Pages 272-291
  6. Back Matter
    Pages 318-355

About this book

Introduction

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern­ ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi­ mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima­ tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

Keywords

Mathematica Parametric statistics Random variable probability statistical theory statistics

Authors and affiliations

  • R.-D. Reiss
    • 1
  1. 1.Fachbereich 6, MathematikUniversität Gesamthochschule SiegenSiegenFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9620-8
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9622-2
  • Online ISBN 978-1-4613-9620-8
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site